December 03, 2020

The first space launch occurred October 4, 1957. What was its name and who launched it?

  • Sputnik I, launched by the Soviet Union

One month later, on November 3, 1957, the first living being was launched into space.

  • Laika the cosmo-dog

It took four more years until the first human was launched into space on April 12, 1961.

  • Yuri Gagarin

And then another eight years for humans to set foot on our Moon on July 20, 1969.

  • NASA’s Apollo 11 crew: Neil Armstrong, Michael Collins, and Buzz Aldrin

Project Goal

  • Determine the relationship between space mission success and other variables.

Space Shuttle Challenger exploded moments after launching on January 28, 1986. Source: CNN news

Data


Source: https://www.kaggle.com/agirlcoding/all-space-missions-from-1957

Exploratory Data Analysis

Launches Over Time

Exploratory Data Analysis

Launch Organizations

Exploratory Data Analysis

Launch Organizations

Exploratory Data Analysis

Launch Countries

Exploratory Data Analysis

Outcome Variable: Launch Success (92%)

Exploratory Data Analysis

Outcome Variable: Launch Success Over Time

Exploratory Data Analysis

Outcome Variable: Launch Success by Country

Exploratory Data Analysis

Outcome Variable: Launch Success by Organization

Method

  • Logistic Regression \[\displaystyle logit(\pi) = log \left( \frac{\pi}{1- \pi} \right) = \beta_0 + \beta_1 X_{1} + \beta_2 X_{2} + \ldots + \beta_k X_{k}\]

  • Binary categorical response variable (yes-no, pass-fail, success-failure, etc.)

Our Models

  • Single Logistic Regression models \[\displaystyle logit(\pi) = log \left( \frac{\pi}{1- \pi} \right) = \beta_0 + \beta_1 X\]

    • Response variable: Mission Outcome (Success: Yes/No)

    • Predictors: Rocket Status (Active/Retired), Country (USA/Russia), Space Race Decade (1960s/1970s)

  • Inferences for the slope term:

    • Determine whether the groups/levels in the explanatory variable differ in chance (odds) of success

Odds Ratio

\[\displaystyle logit(\pi) = log \left( \frac{\pi}{1- \pi} \right) = \beta_0 + \beta_1 X\]

  • Odds of observing a success when \(X = 0\) (reference category): \(e^{\beta_0}\)

  • Odds of observing a success when \(X = 1\) (indicated category): \(e^{\beta_0 + \beta_1} = e^{\beta_0} e^{\beta_1}\)

  • Odds ratio = \(e^{\beta_1}\)

  • Interpretation: odds of a success occurring when \(X = 1\) is OR times greater than when \(X = 0\).

Model: Mission Success and Space Race Decades

Apollo 11

Space Race Decades: 1960s and 1970s

  • Do the two decades differ in terms of successful rate of space mission?

Space Race Decades: 1960s and 1970s

  • Model \[logit(Pr(Success)) = 1.329 + 1.211 \cdot Decade1970s\]
            Estimate Std. Error   z value     Pr(>|z|)
(Intercept) 1.329136 0.08835625 15.042920 3.842221e-51
Decade1970s 1.210549 0.14962088  8.090775 5.928609e-16
  • Untransform (exponentiate) the slope to get odds ratio
Decade1970s Decade1970s 
   1.210549    3.355326
  • 95% confidence interval for OR
   2.5 %   97.5 % 
2.512054 4.519424

Model Fit

\[R^2 = 1 - \frac{Residual \ Deviance}{Null \ Deviance}\]

  • Unlike linear regression…
    • Not the percentage of variability explained by the logistic model, but rather a ratio of how close is the fit to being good or bad.
    • Not related to any correlation coefficient.
Rsq_log_reg <- function(model) {
  1 - model$deviance / model$null.deviance
}
  • Space Race Decade Model: \(R^2 = 0.0508\)

Other Results

  • Active rockets have greater chance of success than retired rockets

(OR = 1.696, 95% CI (1.273, 2.302))

  • Russia is more likely to have successful space missions than USA

(OR = 1.376, 95% CI (1.099, 1.722))

Future Work

  • Quantitative Predictors
  • Other Modeling Methods: Mixed Models, Time Series

Thanks!